Question

Write the anti-derivative of  \[\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right) .\]

Answer 1

\[\int\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right)dx = 3 \frac{x^\frac{1}{2} + 1}{\frac{1}{2} + 1} + \frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} + c\]
\[ = 2 x^\frac{3}{2} + 2 x^\frac{1}{2} + c\]
\[ = 2\left( x^\frac{3}{2} + x^\frac{1}{2} \right) + c\]
\[\text{ Hence , the anti - derivative of  }\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right) \text{ is 2}\left( x^\frac{3}{2} + x^\frac{1}{2} \right) + c .\]